Temperature stresses in a rectangular two-layer plate under the action of a locally distributed temperature field

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dc.citation.epage444
dc.citation.issue2
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage435
dc.contributor.affiliationНаціональний університет “Львівська політехніка”
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.authorМусій, Р. С.
dc.contributor.authorЖидик, У. В.
dc.contributor.authorДрогомирецька, Х. Т.
dc.contributor.authorСвідрак, І. Г.
dc.contributor.authorШиндер, В. К.
dc.contributor.authorMusii, R. S.
dc.contributor.authorZhydyk, U. V.
dc.contributor.authorDrohomyretska, Kh. T.
dc.contributor.authorSvidrak, I. H.
dc.contributor.authorShynder, V. K.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-04T10:28:09Z
dc.date.created2023-02-28
dc.date.issued2023-02-28
dc.description.abstractРозглянуто прямокутну ізотропну двошарову пластину нерегулярної структури, краї якої вільно оперті і на них підтримується стала температура. Для дослідження температурних напружень в пластині використано двовимірні рівняння термопружності типу Кірхгофа і двовимірні рівняння теплопровідності, записані для неоднорідного матеріалу. З використанням методу подвійних тригонометричних рядів за просторовими змінними та інтегрального перетворення Лапласа за часом записано загальні розв’язки крайових задач термопружності і теплопровідності для даної пластини за дії локально розподіленого температурного поля, заданого в початковий момент часу. Числово проаналізовано нормальні напруження в шарах пластини залежно від геометричних параметрів, коефіцієнта тепловіддачі та часу.
dc.description.abstractA rectangular isotropic two-layer plate of an irregular structure is considered, the edges of which are freely supported, and a constant temperature is maintained on them. Two-dimensional Kirchhoff-type thermoelasticity equations and two-dimensional heat equations written for an inhomogeneous material were used to study the temperature stresses in the plate. Using the method of double trigonometric series in spatial variables and the Laplace integral transformation over time, the general solutions of boundary value problems of thermoelasticity and heat conductivity for this plate under the action of a locally distributed temperature field specified at the initial moment of time are written down. The normal stresses in the layers of the plate are numerically analyzed depending on the geometric parameters, heat transfer coefficient, and time.
dc.format.extent435-444
dc.format.pages10
dc.identifier.citationTemperature stresses in a rectangular two-layer plate under the action of a locally distributed temperature field / R. S. Musii, U. V. Zhydyk, Kh. T. Drohomyretska, I. H. Svidrak, V. K. Shynder // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 2. — P. 435–444.
dc.identifier.citationenTemperature stresses in a rectangular two-layer plate under the action of a locally distributed temperature field / R. S. Musii, U. V. Zhydyk, Kh. T. Drohomyretska, I. H. Svidrak, V. K. Shynder // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 2. — P. 435–444.
dc.identifier.doi10.23939/mmc2023.02.435
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/63405
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 2 (10), 2023
dc.relation.ispartofMathematical Modeling and Computing, 2 (10), 2023
dc.relation.references[1] Reddy J. N. Mechanics of laminated composite plates and shells. Theory and analysis. New York, CRC Press (2004).
dc.relation.references[2] Hetnarski R. (ed.) Encyclopedia of Thermal Stresses. Springer, vol. 11 (2014).
dc.relation.references[3] Kolyano Yu. M. Methods of heat conductivity and thermoelasticity of heterogeneous bodies. Кyiv, Naukova dumka (1976).
dc.relation.references[4] Zhydyk U. V., Flyachok V. M. Thermoelastic analysis of heterogeneous anisotropic plates. Scientific notes. 33, 281–287 (2011).
dc.relation.references[5] Brischetto S., Carrera E. Heat conduction and thermal analysis in multilayered plates and shells. Mechanics Research Communications. 38 (6), 449–455 (2011).
dc.relation.references[6] Houari M. S. A., Benyoucef S., Mechab I., Tounsi A., Bedia E. A. A. Two-variable refined plate theory for thermoelastic bending analysis of functionally graded sandwich plates. Journal of Thermal Stresses. 34 (1), 315–334 (2011).
dc.relation.references[7] Naik N. S., Sayyad A. S. An accurate computational model for thermal analysis of laminated composite and sandwich plates. Journal of Thermal Stresses. 42 (5), 559–579 (2019).
dc.relation.references[8] Manthena V. R., Kedar G. D. On thermoelastic problem of a thermosensitive functionally graded rectangular plate with instantaneous point heat source. Journal of Thermal Stresses. 42 (7), 849–862 (2019).
dc.relation.references[9] Manthena V. R., Lamba N. K., Kedar G. D. Transient thermoelastic problem of a nonhomogeneous rectangular plate. Journal of Thermal Stresses. 40 (5), 627–640 (2017).
dc.relation.references[10] Qjuhua L., Hou P., Shang S. Three-dimensional exact analytical solutions of transversely isotropic plate under heat sources. Journal of Thermal Stresses. 44 (11), 1324–1348 (2021).
dc.relation.references[11] Zghal S., Trabelsi S., Frikha A., Dammak F. Thermal free vibration analysis of FG plates and panels with an improved finite shell element. Journal of Thermal Stresses. 44 (3), 315–341 (2021).
dc.relation.references[12] Varelis D., Saravanos D. A. A coupled nonlinear plate finite element for thermal buckling and postbuckling of piezoelectric composite plates including thermo-electro-mechanical effects. Journal of Thermal Stresses. 45 (1), 30–50 (2022).
dc.relation.references[13] Javaheri R., Eslami M. R. Thermal buckling of functionally graded plates. AIAA Journal. 40 (1), 162–169 (2002).
dc.relation.references[14] Hachkevych O. R., Musij R. S., Melnyk N. B., Dmytruk V. A. Dynamic thermoelastic processes in conductive plate under the action of electromagnetic pulses of microsecond and nanosecond durations. Journal of Thermal Stresses. 42 (9), 1110–1122 (2019).
dc.relation.references[15] Musii R. S., Zhydyk U. V., Turchyn Ya. B., Svidrak I. H., Baibakova I. M. Stressed and strained state of the layered cylindrical shell under local convective heating. Mathematical Modeling and Computing. 9(1), 143–151 (2022).
dc.relation.references[16] Thai H.-T., Kim S.-E. A review of theories for the modeling and analysis of functionally graded plates and shells. Composite Structures. 128 (1), 70–86 (2015).
dc.relation.references[17] Swaminathan K., Sangeetha D. M. Thermal analysis of FGM plates – a critical review of various modeling techniques and solution methods. Composite Structures. 160 (1), 43–60 (2017).
dc.relation.referencesen[1] Reddy J. N. Mechanics of laminated composite plates and shells. Theory and analysis. New York, CRC Press (2004).
dc.relation.referencesen[2] Hetnarski R. (ed.) Encyclopedia of Thermal Stresses. Springer, vol. 11 (2014).
dc.relation.referencesen[3] Kolyano Yu. M. Methods of heat conductivity and thermoelasticity of heterogeneous bodies. Kyiv, Naukova dumka (1976).
dc.relation.referencesen[4] Zhydyk U. V., Flyachok V. M. Thermoelastic analysis of heterogeneous anisotropic plates. Scientific notes. 33, 281–287 (2011).
dc.relation.referencesen[5] Brischetto S., Carrera E. Heat conduction and thermal analysis in multilayered plates and shells. Mechanics Research Communications. 38 (6), 449–455 (2011).
dc.relation.referencesen[6] Houari M. S. A., Benyoucef S., Mechab I., Tounsi A., Bedia E. A. A. Two-variable refined plate theory for thermoelastic bending analysis of functionally graded sandwich plates. Journal of Thermal Stresses. 34 (1), 315–334 (2011).
dc.relation.referencesen[7] Naik N. S., Sayyad A. S. An accurate computational model for thermal analysis of laminated composite and sandwich plates. Journal of Thermal Stresses. 42 (5), 559–579 (2019).
dc.relation.referencesen[8] Manthena V. R., Kedar G. D. On thermoelastic problem of a thermosensitive functionally graded rectangular plate with instantaneous point heat source. Journal of Thermal Stresses. 42 (7), 849–862 (2019).
dc.relation.referencesen[9] Manthena V. R., Lamba N. K., Kedar G. D. Transient thermoelastic problem of a nonhomogeneous rectangular plate. Journal of Thermal Stresses. 40 (5), 627–640 (2017).
dc.relation.referencesen[10] Qjuhua L., Hou P., Shang S. Three-dimensional exact analytical solutions of transversely isotropic plate under heat sources. Journal of Thermal Stresses. 44 (11), 1324–1348 (2021).
dc.relation.referencesen[11] Zghal S., Trabelsi S., Frikha A., Dammak F. Thermal free vibration analysis of FG plates and panels with an improved finite shell element. Journal of Thermal Stresses. 44 (3), 315–341 (2021).
dc.relation.referencesen[12] Varelis D., Saravanos D. A. A coupled nonlinear plate finite element for thermal buckling and postbuckling of piezoelectric composite plates including thermo-electro-mechanical effects. Journal of Thermal Stresses. 45 (1), 30–50 (2022).
dc.relation.referencesen[13] Javaheri R., Eslami M. R. Thermal buckling of functionally graded plates. AIAA Journal. 40 (1), 162–169 (2002).
dc.relation.referencesen[14] Hachkevych O. R., Musij R. S., Melnyk N. B., Dmytruk V. A. Dynamic thermoelastic processes in conductive plate under the action of electromagnetic pulses of microsecond and nanosecond durations. Journal of Thermal Stresses. 42 (9), 1110–1122 (2019).
dc.relation.referencesen[15] Musii R. S., Zhydyk U. V., Turchyn Ya. B., Svidrak I. H., Baibakova I. M. Stressed and strained state of the layered cylindrical shell under local convective heating. Mathematical Modeling and Computing. 9(1), 143–151 (2022).
dc.relation.referencesen[16] Thai H.-T., Kim S.-E. A review of theories for the modeling and analysis of functionally graded plates and shells. Composite Structures. 128 (1), 70–86 (2015).
dc.relation.referencesen[17] Swaminathan K., Sangeetha D. M. Thermal analysis of FGM plates – a critical review of various modeling techniques and solution methods. Composite Structures. 160 (1), 43–60 (2017).
dc.rights.holder© Національний університет “Львівська політехніка”, 2023
dc.subjectдвошарова пластина
dc.subjectнерегулярна структура
dc.subjectлокальний теплообмін
dc.subjectтемпературні напруження
dc.subjecttwo-layer plate
dc.subjectirregular structure
dc.subjectlocal heat exchange
dc.subjecttemperature stresses
dc.titleTemperature stresses in a rectangular two-layer plate under the action of a locally distributed temperature field
dc.title.alternativeТемпературні напруження у прямокутній двошаровій пластині за дії локально розподіленого температурного поля
dc.typeArticle

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Mathematical Modeling And Computing. – 2023. – Vol. 10, No. 2